If a stone thrown vertically upwards from a bridge with an initial velocity of $5 \,m \,s^{-1}$ strikes the water below the bridge in a time of $3 \,s$, then the height of the bridge above the water surface is (Acceleration due to gravity $= 10 \,m \,s^{-2}$) (in $\,m$)

Two bodies of masses $m_1$ and $m_2$ are dropped from two different heights $h_1$ and $h_2$ respectively. The ratio of the times taken by the two masses to touch the ground is (neglect air resistance)

$A$ stone is thrown vertically upwards with a velocity $V_0$ from a tower of height $h$ and it reaches the ground in time $t_1$. If the stone is thrown downwards with the same velocity $V_0$ from the same tower,it reaches the ground in time $t_2$. If the stone is dropped from the tower,it reaches the ground in time $t$. Find the value of $t$.

$Assertion$ : $A$ body can have acceleration even if its velocity is zero at a given instant of time.
$Reason$ : $A$ body is momentarily at rest when it reverses its direction.

$A$ ball is thrown vertically upwards with a velocity of $19.6 \, m/s$ from the top of a tower. The ball strikes the ground after $6 \, s$. The height from the ground up to which the ball can rise is given by $\left(\frac{k}{5}\right) \, m$. The value of $k$ is ..... (use $g = 9.8 \, m/s^2$)

If a stone is released from a balloon rising with acceleration $a$ at the instant when its velocity is $v$,then immediately after release,the acceleration and velocity of the stone are